Regularity for solutions of non local parabolic equations

Héctor Chang Lara, Gonzalo Dávila

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

We study the regularity of solutions of parabolic fully nonlinear nonlocal equations. We prove C α regularity in space and time and, under different assumptions on the kernels, C 1,α in space for translation invariant equations. The proofs rely on a weak parabolic ABP and the classic ideas of Tso (Commun. Partial Diff. Equ. 10(5):543-553, 1985) and Wang (Commun. Pure Appl. Math. 45(1), 27-76, 1992). Our results remain uniform as σ → 2 allowing us to recover most of the regularity results found in Tso (Commun. Partial Diff. Equ. 10(5):543-553, 1985). © 2012 Springer-Verlag Berlin Heidelberg.
Original languageEnglish
Pages (from-to)139-172
Number of pages34
JournalCalculus of Variations and Partial Differential Equations
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

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